The velocity v at time t of an object travelling in a straight line is given by v = t - 3. Determine the distance it travels from t = 0 and t = 4.
$\displaystyle \frac{dx}{dt} = t - 3 \Rightarrow x = \frac{t^2}{2} - 3t + C$.
Assume x(0) = 0: $\displaystyle x = \frac{t^2}{2} - 3t$.
Note: The answer is NOT x(4) - x(0). Why?
Distance travelled = $\displaystyle \frac{9}{2} + \left( \frac{9}{2} - 4\right) = .....$
Draw a graph of x versus t to see this.